Average Error: 0 → 0
Time: 27.8s
Precision: 64
Internal Precision: 384
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right) + \left(\left(\left(\left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(20 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(1 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(\left(-1 + 1 i \cdot \left(15 \cdot -1 + 1 i\right) + \left(\left(\left(\left(\left(-1 + 1 i \cdot \left(\left(-1 + 1 i \cdot 6\right) \cdot -1 + 1 i\right)\right) \cdot -1 + 1 i\right) \cdot -1 + 1 i + -1 + 1 i \cdot \left(-1 + 1 i \cdot \left(-1 + 1 i \cdot \left(-1 + 1 i \cdot \left(-1 + 1 i \cdot -1 + 1 i\right)\right)\right)\right)\right) + -1 + 1 i \cdot \left(-1 + 1 i \cdot \left(-1 + 1 i \cdot \left(15 \cdot -1 + 1 i\right)\right)\right)\right) + \left(\left(20 \cdot -1 + 1 i\right) \cdot -1 + 1 i\right) \cdot -1 + 1 i\right)\right) + -1 + 1 i \cdot 6\right) + 1\right))\]

Error

Derivation

  1. Initial program 0

    \[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right) + \left(\left(\left(\left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(20 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(1 + 0 i\right)\right))\]

  2. Applied simplify0

    \[\leadsto \color{blue}{\Im(\left(\left(\left(-1 + 1 i \cdot \left(15 \cdot -1 + 1 i\right) + \left(\left(\left(\left(\left(-1 + 1 i \cdot \left(\left(-1 + 1 i \cdot 6\right) \cdot -1 + 1 i\right)\right) \cdot -1 + 1 i\right) \cdot -1 + 1 i + -1 + 1 i \cdot \left(-1 + 1 i \cdot \left(-1 + 1 i \cdot \left(-1 + 1 i \cdot \left(-1 + 1 i \cdot -1 + 1 i\right)\right)\right)\right)\right) + -1 + 1 i \cdot \left(-1 + 1 i \cdot \left(-1 + 1 i \cdot \left(15 \cdot -1 + 1 i\right)\right)\right)\right) + \left(\left(20 \cdot -1 + 1 i\right) \cdot -1 + 1 i\right) \cdot -1 + 1 i\right)\right) + -1 + 1 i \cdot 6\right) + 1\right))}\]

Runtime

Time bar (total: 27.8s)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' 
(FPCore ()
  :name "3.9.1 imaginary part (p56)"
  (im (+ (+ (+ (+ (+ (+ (* (* (* (* (* (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (* (* (* (* (* (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (* (* (* (* (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (* (* (* (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (* (* (complex 15 0) (complex -1 1)) (complex -1 1))) (* (complex 6 0) (complex -1 1))) (complex 1 0))))